(5x-6) squared please answer
2 answers:
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Answer:
0.1056 = 10.56% probability that their average salary is more than $77,500.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean $75,000 and standard deviation $8,000.
This means that
Sample of 16
This means that
What is the probability that their average salary is more than $77,500?
This is 1 subtracted by the pvalue of Z when X = 77500. So
By the Central Limit Theorem
has a pvalue of 0.8944
1 - 0.8944 = 0.1056
0.1056 = 10.56% probability that their average salary is more than $77,500.
<h3>Answer: Choice D</h3>
Explanation:
Start at the arrow tip. Move vertically until reaching the x axis. You'll arrive at x = 7 which is the x component of the vector.
Go back to the arrow tip. This time move horizontally until reaching the y axis, so you should arrive at y = -6
Therefore the vector is which is in a column vector format. A row vector would have the numbers listed horizontally.
Put another way, the arrow tip is at the point location of (7,-6). This leads directly to the column vector mentioned in the previous paragraph.